PHY 150 Project One Supply Drop Plan
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School
Southern New Hampshire University *
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Course
150
Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
docx
Pages
4
Uploaded by DukeFlower6233
A&L ENGINEERING
Supply Drop Plan
Horizontal and Vertical Motion
Diagram
Kinematics Calculations
y = y
o + v
yo
t + 1/2a
y
t
2
2650=0+1/2(9.8)t
2
2650=4.9t
2
t=(2650/4.9)
1/2
=23.26 s
250 mi/hr * 1609 m/mi
/ 3600 s/hr = 111.74 m/s
x=v
xo
t
x=111.74 m/s
(23.26 s) = 2599.07 m
Equation Descriptions
Vertical motion can be calculated using y = y
o + v
yo
t + 1/2a
y
t
2
where y = altitude of plane in meters,
2599
.
07
m
Velocity of plane =250 mi/hr
y
o
= initial distance of payload from plane
v
yo
= initial velocity of the payload
t = the time from payload release to touchdown
a
y = acceleration of the payload due to gravity (9.8 m/s
2
).
Adaptations for Scenario One
Diagram
Adaptation Description
Windspeed in Portland, ME on 1/29/2024 is 10 mph
Convert headwind to m/s.
10 mi/hr * 1609 m/mi
/ 3600 s/hr = 4.47 m/s
Subtract headwind from original velocity.
111.74 m/s – 4.47 m/s
= 107.27 m/s
Multiply new velocity by time for payload to reach dropdown.
107.27
* 23.26 = 2495.10
Adaptations for Scenario Two
Diagram
2495.10
m
Headwind = 10 mi/hr
Adaptation Description
In this scenario, the catapult is 50 m below, and 400 m
away from the dropsite. Its velocity is 67 m/s
with a trajectory of +50
o
.
v
x
= 67cos(50
o
) = 43.07
v
y
= 67sin(50
o
) = 51.32
y = y
o
+ v
y
t + 1/2at
2
50 = 51.32t - 4.9t
2
0 = -4.9t
2
+ 51.32t – 50
t = (-51.32 – ((51.32
2
– 4(-4.9)(-50))
1/2
) / -9.8
t = (-51.32-((2633.74 – 980)
1/2
) / -9.8
t = (-51.32 – ((1653.74)
1/2
) / -9.8
t = (-51.32 – 40.67) / -9.8
t = -91.99 / -9.8
t = 9.39
displacement = 43.07(9.39)
displacement = 404.43
The catapult would be sufficient to deliver the payload to the dropsite.
50 m
400 m
67 m/s
50 deg
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References
Urone, P. P., & Hinrichs, R. (n.d.). Ch. 2 introduction to one-dimensional kinematics - college physics 2E
. OpenStax. https://openstax.org/books/college-physics-2e/pages/2-introduction-
to-one-dimensional-kinematics Urone, P. P., & Hinrichs, R. (n.d.-a). 2.7 falling objects - college physics 2E
. OpenStax. https://openstax.org/books/college-physics-2e/pages/2-7-falling-objects Minton, L. (n.d.). National Weather Service : Observed weather for past 3 Days : Portland, Portland international jetport. https://w1.weather.gov/data/obhistory/KPWM.html